It will work, and could very well prove to give accurate rounds. But if you are loading at your own home on one press during the week, then loading at GF's place on weekends on a different press, you may find it challenging to keep the same die adjustments. Using 2 different tool sets? Not ideal. It's real easy to blame any accuracy issues on "the cheap press" but there are other issues at play, as well. My thinking is that, more important than the price of the press or dies, consistency is key to accurate ammo. Consistency in your techniques and in your tools leads to consistency in your loading.
If it were me, I would load the competition rounds on your home set and load plinking ammo on the set at GF's place. Y'know, it was real sweet of her to get you some tools to use at her place, just so she could spend more time with you. Don't let her see any disappointment from you about her choice of purchase. She sounds like a keeper.